First of all,..... who am I. I am just a fellow allergy sufferer, with an opinion based on my own understanding of allergies and my own experiences. The most important opinion is your own, for you are going to be responsible for protecting your child from things that you can neither see or understand, or things that you can see. Not an easy job!
Your daughter might not be able to understand why she feels a certain way, and not be able to tell that her lack of energy, or sluggishness, is not a normal way of feeling.
To understand, you need to understand how allergies and the Immune System and the NeuroHormonal System co-exist. When you come into contact with an allergen, like the odor of a dog, the Immune System and the NeuroHormonal Systems pumps chemicals (cytokines, hormones) into the body. It's this "protective" chemical mix that makes allergy sufferers feel so bad, and feel like they have a cold. These body chemicals can cause an inordinate amount of stress and discomfort on one's body, and lead to behavior problems, sluggishness, not feeling well (malaise), mental confusion, hyperactivity, etc.
As one "outgrows" an allergy, all it means, IMHO, is that the body has been able to prevent a sinus or asthma attack through the release of sufficient body chemicals. So...... instead of having an allergic reaction to a pet, the body is going to react to the chemicals. When you are young and your immune system and metabolism is strong, you don't have as severe a reaction to these body chemicals. When you get up there in age, like me nearing 70, with a weakening immune system,etc., you can really notice the negative impact of these excess body chemicals.

:dizzy:
My Asthma and Sinus problems are under reasonable control via Flovent. My main problem is with the excess body chemicals, which make me sick as a dog (pardon the expression).
Poor little tyke. I hope that she recovers quickly and is up and about and driving her parents nuts once again!
Here is my bottom line: The closer the contact with the offending allergy, be it pet or other irritant, the worse it is for the allergy sufferer. If the dog is anywhere in the home, it means that your daughter is ALWAYS being subjected to a full dose of dog allergy. You can close doors, you can lock the dog up in the basement. It doesn't matter, because tiny odors/allergens from the pet will somehow seep into her location and constantly attack her Immune System. Her tiny little body's Immune System will never have a chance to rest and recover as long as the dog is anywhere in the home.
I'm sure that you've heard the story of a child on a plane in first class that has an extreme allergic reaction to a peanut being eaten near the back of the plane. This is the way that allergies work, except in many cases the reaction isn't as severe. All it takes is an absurdly tiny, trace amount of allergen to set off the allergic/Immune System process.
So..... the ball is in your court. Do you want to take the chance that the dog allergy is not negatively effecting your daughter? Are you a betting or garabling person? Would it not be just simpler to not take even the slightest chance, with your daughter's health and well-being, and get rid of the dog before your daughter forms a stronger bond with the dog? How do you know for sure that the dog isn't worsening her current health problem?
Best of luck to your family and your child.
Take care................. :wave: